Overview
- Offers the first unified treatment of generalized multiresolution analyses and wavelet theory
- Illustrates the author’s pioneering constructions of wavelet sets
- Facilitates an abstract understanding of wavelet sets and frames by using the GMRA formulation
- Generalizes classical wavelet techniques in L^2(R) and beyond to abstract spaces
Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)
Part of the book sub series: Lecture Notes in Applied and Numerical Harmonic Analysis (LN-ANHA)
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Table of contents (8 chapters)
Keywords
About this book
Beginning with the basic properties of GMRAs, the book goes on to explore the multiplicity and dimension functions of GMRA, wavelet sets, and generalized filters. The author’s constructions of wavelet sets feature prominently, with figures to illustrate their remarkably simple geometric form. The last three chapters exhibit extensions of wavelet theory and GMRAs to other settings. These include fractal spaces, wavelets with composite dilations, and abstract constructions of GMRAs beyond the usual setting of L2(ℝn).
This account of recent developments in wavelet theory will appeal to researchers and graduate students with an interest in multiscale analysis from a pure or applied perspective. Familiarity with harmonic analysis and operator theory will be helpful to the reader, though the only prerequisite is graduate level experience with real and functional analysis.
Reviews
“It is well-suited for graduate students who want to become familiar with this interesting topic and to researchers who would like to get a quick overview over the area.” (Peter Massopust, zbMATH 1409.42001, 2019)
Authors and Affiliations
Bibliographic Information
Book Title: Generalized Multiresolution Analyses
Authors: Kathy D. Merrill
Series Title: Applied and Numerical Harmonic Analysis
DOI: https://doi.org/10.1007/978-3-319-99175-7
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-319-99174-0Published: 12 October 2018
eBook ISBN: 978-3-319-99175-7Published: 11 October 2018
Series ISSN: 2296-5009
Series E-ISSN: 2296-5017
Edition Number: 1
Number of Pages: X, 113
Number of Illustrations: 17 b/w illustrations
Topics: Abstract Harmonic Analysis, Functional Analysis, Measure and Integration